论文标题
mod $ 4 $单峰序列的证明和相关的模拟theta功能
A proof of the mod $4$ unimodal sequence conjectures and related mock theta functions
论文作者
论文摘要
2012年，布赖森（Bryson），ono，pitman和Rhoades展示了某些强烈单峰序列的生成函数如何与量子模块和模块化模块形式有关。他们证明了一些奇偶校验结果，并猜想了一些Mod 4的一致性，这些生成功能的系数。在2016年，Kim，Lim和Lovejoy获得了奇特平衡的单峰序列的相似结果，并做出了类似的MOD 4猜想。我们证明了所有这些mod 4的猜想和类似的一致性Andrews spt功能和相关的模拟theta函数。我们的证明方法涉及新的Hecke-Rogers类型身份，用于不确定的二进制二进制形式和Hurwitz班级编号。
In 2012 Bryson, Ono, Pitman and Rhoades showed how the generating functions for certain strongly unimodal sequences are related to quantum modular and mock modular forms. They proved some parity results and conjectured some mod 4 congruences for the coefficients of these generating functions. In 2016 Kim, Lim and Lovejoy obtained similar results for odd-balanced unimodal sequences and made similar mod 4 conjectures. We prove all of these mod 4 conjectures and similar congruences for the Andrews spt-function and related mock theta functions. Our method of proof involves new Hecke-Rogers type identities for indefinite binary quadratic forms and the Hurwitz class number.
